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f(x) = 1 over x
f(x) = b
f(x) = cube root of x
f(x) = IxI
f(x) = squared root of x
f(x) = x
f(x) = x^2
f(x) = x^3
Real World Applications for Algebraic Functions
Transformations
Vertex and Axis Symmetry of a Quadratic Function
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Transformations
f(x) =x^2
Basic Graph:
Vertical Shift Down:
Horizontal Shift - Right:
Reflect across X-axis: f(x) = -x^2
f(x) = x^(1/2) Basic graph: Reflect across Y-axis:
Vertical stretch: f(x) = IxI Basic Graph: Vertical stretch: f(x) = 2IxI Graph:
Combination of 3: f(x) = x^2:
Transformations from
x^2
to
-x^2
to
(x-4)^2
to
(x+2)^2-5
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Transformations
f(x) =x^2
Basic Graph:
Vertical Shift Down:
Horizontal Shift - Right:
Reflect across X-axis: f(x) = -x^2
f(x) = x^(1/2) Basic graph: Reflect across Y-axis:
Vertical stretch: f(x) = IxI Basic Graph: Vertical stretch: f(x) = 2IxI Graph:
Combination of 3: f(x) = x^2:
Transformations from x^2 to -x^2 to (x-4)^2 to (x+2)^2-5